کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9492850 1333840 2005 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Two-sided ideals in q-deformed Heisenberg algebras
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Two-sided ideals in q-deformed Heisenberg algebras
چکیده انگلیسی
In this article, the structure of two-sided ideals in the q-deformed Heisenberg algebras defined by the q-deformed Heisenberg canonical commutation relationAB-qBA=Iis investigated. We show that these algebras are simple if and only if q=1. For q≠1,0 we present an infinite descending chain of non-trivial two-sided ideals, thus deducing by explicit construction that the q-deformed Heisenberg algebras are not just non-simple but also non-artinian for q≠1,0. We establish a connection between the quotients of the q-deformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in q-deformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in q-deformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of q-deformed Heisenberg algebras.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 23, Issue 2, 1 June 2005, Pages 99-125
نویسندگان
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